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User:Moremajorthanmajor/17edX: Difference between revisions

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Line 1: Line 1:
==Intervals==
'''17edX''' means division of a tenth interval into 17 equal parts.
 
== Intervals ==
{| class="wikitable"
{| class="wikitable"
! rowspan="5" |Degrees
! Decade
! colspan="4" rowspan="5" |Enneatonic
!Period
! colspan="8" |Minor mode Middletown temperament
!Notes
! colspan="2" |Neutral mode Middletown temperament
! colspan="10" |Major mode Middletown temperament
|-
|-
! colspan="2" rowspan="3" |Aeolian-Dorian
| 6\5
! colspan="6" |Dorian
|''84.706''
! colspan="2" rowspan="3" |Dorian-Mixolydian
|Intense Aeolian-Subpental Dorian mode begins
! colspan="8" |Mixolydian
! colspan="2" rowspan="3" |Mixolydian-Ionian
|-
|-
! colspan="2" rowspan="2" |Subpental
|29\24
! colspan="2" rowspan="2" |Pental
|''85.294''
! colspan="2" rowspan="2" |Superpental
|
! colspan="2" rowspan="2" |Subpental
! colspan="2" rowspan="2" |Pental
! colspan="4" |Superpental
|-
|-
! colspan="2" |Soft
|23\19
! colspan="2" |Intense
|85.449
|
|-
|-
! |Minimum
|17\14
! |Maximum
|85.714
!Minimum
|
!Maximum
|-
!Minimum
|11\9
!Maximum
|86.275
!Minimum
|Intense Aeolian-Subpental Dorian mode ends, Subpental Dorian mode begins
!Maximum
|-
!Minimum
|16\13
! |Maximum
|86.878
!Minimum
|
!Maximum
|-
! |Minimum
|21\17
!Maximum
|87.197
!Minimum
|
!Maximum
|-
!Minimum
|5\4
!Maximum
|''88.235''
!Minimum
|Subpental Dorian mode ends, Pental Dorian mode begins
! |Maximum
|-
|24\19
|89.164
|
|-
|19\15
|89.412
|
|-
|14\11
|89.840
|Pental Dorian mode ends, Superpental Dorian mode begins
|-
|23\18
|90.196
|
|-
|9\7
|90.756
|Superpental Dorian mode ends, Mohajira Dorian-Mixolydian mode begins
|-
|31\24
|''91.176''
|
|-
|22\17
|91.349
|Mohajira Dorian-Mixolydian mode ends, Beatles Dorian-Mixolydian mode begins
|-
|35\27
|91.503
|
|-
|13\10
|91.765
|Beatles Dorian-Mixolydian mode ends, Subpental Mixolydian mode begins
|-
|17\13
|92.308
|
|-
|21\16
|92.647
| Subpental Mixolydian mode ends, Pental Mixolydian mode begins
|-
|25\19
|92.879
|
|-
|29\22
|93.048
|
|-
|33\25
|93.176
|
|-
|4\3
|''94.118''
|Pental Mixolydian mode ends, Soft Superpental Mixolydian mode begins
|-
|19\14
|95.798
|
|-
|15\11
|96.257
|Soft Superpental Mixolydian mode ends, Intense Superpental Mixolydian mode begins
|-
|26\19
|96.594
|
|-
|11\8
|''97.059''
|Intense Superpental Mixolydian mode ends, Mixolydian-Ionian mode begins
|-
|18\13
|97.738
|
|-
|25\18
|98.032
|
|-
|7\5
|98.824
|Mixolydian-Ionian mode ends
|}Golden/Pyrite Tunings±13¢
 
{| class="wikitable" style="text-align: center"
! rowspan="2" |Degrees
! colspan="4" rowspan="2" |Enneatonic
! rowspan="2" |Intense Aeolian-Subpental Dorian
! colspan="3" |Dorian
|-
!Subpental
!Pental
!Superpental
|-
| |1
|J
|''A''
|Jb
|''Ab''
|85.109-86.638
|85.932-87.462
|88.7805-90.6955
|89.334-90.863
|-
| |2
|A\\
|''B\\''
| colspan="2" |G#
|170.218-173.277
|171.865-174.9235
|177.561-180.62
|178.667-181.726
|-
| |3
|Jp
|''Ap''
|J
|''A''
|255.327-259.915
|257.797-262.385
|266.341-270.93
|268.001-272.589
|-
| |4
|J
|''B''
|A
|''B''
|340.4355-346.553
|343.729-349.847
|355.122-361.2395
|357.335-363.452
|-
| |5
|B
|''C''
|Bb
|''Cb''
|425.544-433.1915
|429.662-437.309
|442.902-451.5495
|446.668-454.315
|-
| |6
|C\\
|''Q\\''
|A#
|''B#''
|510.653-519.83
|515.594-524.7705
|532.683-541.859
|536.002-545.178
|-
| |7
|Bp
|''Cp''
|B
|''C''
|595.762-606.468
|601.526-612.232
|621.463-632.169
|625.3355-636.041
|-
|8
|C
|''Q''
|C
|''Q''
|680.871-693.106
|687.459-699.694
|710.244-722.479
|714.996-726.904
|-
|9
|Q
|''D''
|Qb
|Db
|765.98-779.745
|773.391-787.156
|799.024-812.789
|804.003-817.768
|-
|10
|D\\
|''Q\\''
|C#
|Q#
|851.089-866.383
|859.323-874.6175
|887.805-903.099
|893.336-999.4935
|-
|11
|Qp
|''Dp''
|Q
|''D''
|936.198-953.021
|945.256-962.079
|976.585-993.409
|982.67-1090.357
|-
|12
| colspan="2" |D
|D
|''S''
|1021.3065-1039.66
|1031.188-1049.541
|1065.366-1083.719
|1072.004-1181.22
|-
|13
|E
|''S''
| colspan="2" |Eb
|1106.415-1186.94
|1117.12-1137.003
|1154.146-1174.029.
|1161.337-1272.083
|-
|14
| colspan="2" |F
|D#
|''S#''
|1191.524-1212.936
|1203.052-1224.464
|1242.927-1264.3385
|1250.671-1362.946
|-
|15
| colspan="2" |G\\
| colspan="2" |E
|1276.633-1299.5745
|1288.985-1311.926
|1331.707-1354.648
|1340.005-1453.809
|-
|16
| colspan="2" |Fp
| colspan="2" |F
|1361.741-1386.213
|1374.917-1399.388
|1420.488-1424.958
|1426.338-1453.809
|-
|17
| colspan="4" |G
|1446.851-1472.851
|1460.85-1486.85
|1509.268-1535.268
|1518.672-1544.672
|}
{| class="wikitable" style="text-align: center"
!Degrees
! colspan="8" |Enneatonic
!Mohajira
!Beatles
|-
|-
| |1
| |1
| colspan="2" |G
| colspan="2" |G
| colspan="2" |Gb
| colspan="2" |Gb
| |84.706
|J
| colspan="2" |86.2745
|''A''
| colspan="2" |88.235
|Jb
| colspan="2" |89.84
|''Ab''
| colspan="2" |90.756
|90.464-91.994
| colspan="2" |91.765
|90.6955-92.225
| colspan="2" |92.647
| colspan="2" |94.118
| colspan="2" |94.929
| colspan="2" |97.363
| |98.8235
|-
|-
| |2
| |2
Line 63: Line 317:
|''A\\''
|''A\\''
| colspan="2" |F#
| colspan="2" |F#
| |169.412
|A\\
| colspan="2" |172.549
|''B\\''
| colspan="2" |176.471
| colspan="2" |G#
| colspan="2" |179.679
|180.929-183.988
| colspan="2" |181.513
|181.391-184.45
| colspan="2" |183.528
| colspan="2" |185.294
| colspan="2" |188.235
| colspan="2" |189.858
| colspan="2" |194.726
| |197.647
|-
|-
| |3
| |3
| colspan="2" |Gp
| colspan="2" |Gp
| colspan="2" |G
| colspan="2" |G
| |254.118
|Jp
| colspan="2" |258.8235
|''Ap''
| colspan="2" |264.706
|J
| colspan="2" |269.519
|''A''
| colspan="2" |272.268
|271.393-275.9815
| colspan="2" |275.294
|272.086-276.675
| colspan="2" |277.941
| colspan="2" |282.353
| colspan="2" |284.787
| colspan="2" |292.089
| |296.471
|-
|-
| |4
| |4
Line 95: Line 338:
|J
|J
|''A''
|''A''
| |338.823'5
|J
| colspan="2" |345.098
|''B''
| colspan="2" |352.941
|A
| colspan="2" |359.358
|''B''
| colspan="2" |363.025
|361.858-367.975
| colspan="2" |367.059
|362.782-368.91
| colspan="2" |370.588
| colspan="2" |376.471
| colspan="2" |379.716
| colspan="2" |389.452
| |395.294
|-
|-
| |5
| |5
Line 112: Line 350:
|Ab
|Ab
|''Bb''
|''Bb''
| |423.529
|B
| colspan="2" |431.3725
|''C''
| colspan="2" |441.1765
|Bb
| colspan="2" |449.198
|''Cb''
| colspan="2" |453.7815
|452.322-459.969
| colspan="2" |458.8235
|453.477-461.124
| colspan="2" |463.235
| colspan="2" |470.588
| colspan="2" |474.645
| colspan="2" |486.815
| |494.118
|-
|-
| |6
| |6
Line 129: Line 362:
|J#
|J#
|''A#''
|''A#''
| |508.235
|C\\
| colspan="2" |517.647
|''Q\\''
| colspan="2" |529.412
|A#
| colspan="2" |539.037
|''B#''
| colspan="2" |544.538
|542.787-551.963
| colspan="2" |550.588
|544.173-553.349
| colspan="2" |555.882
| colspan="2" |564.706
| colspan="2" |569.574
| colspan="2" |584.1785
| |592.941
|-
|-
| |7
| |7
Line 146: Line 374:
|A
|A
|''B''
|''B''
| |592.941
|Bp
| colspan="2" |603.921
|''Cp''
| colspan="2" |617.647
|B
| colspan="2" |628.877
|''C''
| colspan="2" |635.394
|633.251-643.957
| colspan="2" |642.353
|634.868-645.574
| colspan="2" |648.529
| colspan="2" |658.8235
| colspan="2" |664.503
| colspan="2" |681.542
| |691.765
|-
|-
|8
|8
Line 163: Line 386:
|B
|B
|''H''
|''H''
|677.647
|C
| colspan="2" |690.169
|''Q''
| colspan="2" |705.882
|C
| colspan="2" |718.717
|''Q''
| colspan="2" |726.05
|723.7155-735.951
| colspan="2" |734.118
|725.564-737.799
| colspan="2" |741.1765
| colspan="2" |752.941
| colspan="2" |759.432
| colspan="2" |778.905
|790.588
|-
|-
|9
|9
Line 180: Line 398:
|Hb
|Hb
|''Cb''
|''Cb''
|762.653
|Q
| colspan="2" |776.471
|''D''
| colspan="2" |794.118
|Qb
| colspan="2" |808.556
|Db
| colspan="2" |816.806
|814.18-827.945
| colspan="2" |825.882
|816.259-830.024
| colspan="2" |833.8235
| colspan="2" |847.059
| colspan="2" |854.361
| colspan="2" |876.268
|889.412
|-
|-
|10
|10
Line 197: Line 410:
|B#
|B#
|''H#''
|''H#''
|847.059
|D\\
| colspan="2" |862.745
|''Q\\''
| colspan="2" |882.353
|C#
| colspan="2" |898.396
|Q#
| colspan="2" |907.563
|904.644-919.9385
| colspan="2" |917.647
|906.955-922.289
| colspan="2" |926.471
| colspan="2" |941.1765
| colspan="2" |949.29
| colspan="2" |973.631
|988.235
|-
|-
|11
|11
Line 214: Line 422:
|H
|H
|''C''
|''C''
|931.765
|Qp
| colspan="2" |949.02
|''Dp''
| colspan="2" |970.588
|Q
| colspan="2" |988.235
|''D''
| colspan="2" |998.319
|995.109-1011.932
| colspan="2" |1009.412
|997.65-1014.474
| colspan="2" |1019.118
| colspan="2" |1035.294
| colspan="2" |1044.219
| colspan="2" |1070.994
|1087.059
|-
|-
|12
|12
Line 231: Line 434:
|C
|C
|''D''
|''D''
|1016.471
| colspan="2" |D
| colspan="2" |1035.294
|D
| colspan="2" |1058.8235
|''S''
| colspan="2" |1078.075
|1085.573-1103.926
| colspan="2" |1089.076
|1088.346-1106.699
| colspan="2" |1101.1765
| colspan="2" |1111.765
| colspan="2" |1129.412
| colspan="2" |1139.148
| colspan="2" |1168.357
|1185.882
|-
|-
|13
|13
Line 248: Line 445:
|Db
|Db
|''Sb''
|''Sb''
|1101.1765
|E
| colspan="2" |1121.569
|''S''
| colspan="2" |1147.059
| colspan="2" |Eb
| colspan="2" |1167.914
|1176.038-1195.92
| colspan="2" |1179.832
|1179.041-1198.9235
| colspan="2" |1192.941
| colspan="2" |1204.412
| colspan="2" |1223.529
| colspan="2" |1234.077
| colspan="2" |1265.72
|1284.706
|-
|-
|14
|14
Line 264: Line 455:
|C#
|C#
|''D#''
|''D#''
|1185.882
| colspan="2" |F
| colspan="2" |1027.843
|D#
| colspan="2" |1235.294
|''S#''
| colspan="2" |1257.754
|1266.502-1287.914
| colspan="2" |1270.588
|1269.737-1291.1485
| colspan="2" |1284.706
| colspan="2" |1297.059
| colspan="2" |1317.647
| colspan="2" |1329.006
| colspan="2" |1363.083
|1383.529
|-
|-
|15
|15
Line 280: Line 465:
|D
|D
|''S''
|''S''
|1270.588
| colspan="2" |G\\
| colspan="2" |1294.118
| colspan="2" |E
| colspan="2" |1323.529
|1356.967-1379.908
| colspan="2" |1347.594
|1360.432-1383.373
| colspan="2" |1361.3445
| colspan="2" |1376.471
| colspan="2" |1389.706
| colspan="2" |1411.765
| colspan="2" |1423.935
| colspan="2" |1460.446
|1482.352
|-
|-
|16
|16
| colspan="2" |Ep
| colspan="2" |Ep
| colspan="2" |E
| colspan="2" |E
|1355.294
| colspan="2" |Fp
| colspan="2" |1380.392
| colspan="2" |F
| colspan="2" |1411.765
|1447.431-1471.902
| colspan="2" |1437.433
|1451.128-1475.598
| colspan="2" |1452.101
| colspan="2" |1468.235
| colspan="2" |1482.353
| colspan="2" |1505.882
| colspan="2" |1518.864
| colspan="2" |1557.809
|1581.1765
|-
|-
|17
|17
| colspan="2" |F
| colspan="4" |F
| colspan="2" |F
| colspan="4" |G
|1440
|1537.8955-1563.8955
| colspan="2" |1466.667
|1541.823-1577.823
| colspan="2" |1500
|}
| colspan="2" |1527.273
{| class="wikitable" style="text-align: center"
| colspan="2" |1542.857
! rowspan="3" |Degrees
| colspan="2" |1560
! colspan="4" rowspan="3" |Enneatonic
| colspan="2" |1575
| colspan="2" |1600
| colspan="2" |1613.793
| colspan="2" |1655.172
|1680
|}Golden tunings
{| class="wikitable"
|+
! rowspan="4" |Degrees
! colspan="4" rowspan="4" |Enneatonic
! colspan="4" |Minor mode Middletown temperament
!Neutral mode Middletown temperament
! colspan="5" |Major mode Middletown temperament
|-
! rowspan="3" |Aeolian-Dorian
! colspan="3" |Dorian
! rowspan="3" |Dorian-Mixolydian
! colspan="4" |Mixolydian
! colspan="4" |Mixolydian
! rowspan="3" |Mixolydian-Ionian
! rowspan="3" |Mixolydian-Ionian
|-
|-
! rowspan="2" |Subpental
! rowspan="2" |Pental
! rowspan="2" |Superpental
! rowspan="2" |Subpental
! rowspan="2" |Subpental
! rowspan="2" |Pental
! rowspan="2" |Pental
Line 346: Line 497:
!Intense
!Intense
|-
|-
|1
| |1
| colspan="2" |G
| colspan="2" |G
| colspan="2" |Gb
| colspan="2" |Gb
|85.874
|92.019-93.548
|86.697
|92.035-93.5645
|89.545
|94.1155-95.645
|90.098
|95.669-97.198
|91.46
|96.739-98.268
|92.401
|92.8
|94.88
|96.433
|97.504
|-
|-
|2
| |2
|J\\
|J\\
|''A\\''
|''A\\''
| colspan="2" |F#
| colspan="2" |F#
|171.747
|184.038-187.139
|173.394
|184.07-187.129
|179.09
|188.231-191.29
|180.197
|191.337-194.396
|182.92
|193.478-196.537
|184.802
|185.6
|189.7605
|192.867
|195.007
|-
|-
|3
| |3
| colspan="2" |Gp
| colspan="2" |Gp
| colspan="2" |G
| colspan="2" |G
|257.621
|276.0565-280.645
|260.091
|276.105-280.693
|268.636
|282.347-286.935
|270.295
|287.006-291.594
|274.381
|290.217-294.805
|277.204
|278.399
|284.641
|289.3
|292.511
|-
|-
|4
| |4
|J
|J
|A
|A
|J
|J
|''A''
|''A''
|343.494
|368.075-374.193
|346.788
|368.14-374.258
|358.181
|376.462-382.58
|360.393
|382.675-388.792
|365.841
|386.956-393.074
|369.605
|371.199
|379.521
|385.733
|390.015
|-
|-
|5
| |5
|A
|A
|''B''
|''B''
|Ab
|Ab
|''Bb''
|''Bb''
|429.368
|460.094-467.741
|433.485
|460.175-467.822
|447.726
|470.578-478.225
|450.492
|478.343-485.99
|457.301
|483.695-491.342
|462.006
|463.999
|474.401
|482.167
|487.519
|-
|-
|6
| |6
|B\\
|B\\
|''H\\''
|''H\\''
|J#
|J#
|''A#''
|''A#''
|515.2415
|552.113-561.29
|520.182
|552.21-561.387
|537.271
|564.693-573.87
|540.59
|574.012-583.188
|548.761
|580.434-589.6105
|554.407
|556.799
|569.2815
|578.6
|585.022
|-
|-
|7
| |7
|Ap
|Ap
|''Bp''
|''Bp''
|A
|A
|''B''
|''B''
|601.115
|644.132-654.838
|606.879
|644.2455-654.951
|626.516
|658.809-669.515
|630.688
|669.6805-680.386
|640.221
|677.173-687.879
|646.808
|649.598
|664.162
|675.033
|682.526
|-
|-
|8
|8
Line 458: Line 574:
|B
|B
|''H''
|''H''
|686.989
|736.151-748.386
|693.576
|736.281-748.516
|716.3615
|752.924-765.16
|720.787
|765.349-777.584
|731.6815
|773.912-783.147
|739.21
|742.398
|759.042
|771.467
|780.03
|-
|-
|9
|9
Line 474: Line 585:
|Hb
|Hb
|''Cb''
|''Cb''
|772.862
|828.17-841.934
|780.273
|828.316-842.08
|805.907
|847.04-860.805
|810.885
|861.018-874.7852
|823.142
|870.416-884.416
|831.611
|835.198
|853.922
|867.9
|877.5335
|-
|-
|10
|10
Line 490: Line 596:
|B#
|B#
|''H#''
|''H#''
|858.736
|920.1885-935.483
|866.97
|920.351-935.645
|895.452
|941.155-956.45
|900.983
|956.6865-971.9805
|914.602
|967.39-982.684
|924.012
|927.998
|948.8025
|964.3335
|975.037
|-
|-
|11
|11
Line 506: Line 607:
|H
|H
|''C''
|''C''
|944.609
|1012.207-1029.031
|953.667
|1012.386-1029.209
|984.997
|1035.271-1052.0945
|991.082
|1052.355-1069.179
|1006.062
|1064.129-1080.953
|1016.413
|1020.7975
|1043.683
|1060.767
|1072.541
|-
|-
|12
|12
Line 522: Line 618:
|C
|C
|''D''
|''D''
|1030.483
|1104.226-1122.579
|1040.3645
|1104.421-1122.774
|1074.542
|1129.3865-1147.7395
|1081.18
|1148.024-1166.377
|1097.522
|1160.868-1179.221
|1108.814
|1113.567
|1138.563
|1157.2
|1170.045
|-
|-
|13
|13
Line 538: Line 629:
|Db
|Db
|''Sb''
|''Sb''
|1116.3565
|1196.245-1216.127
|1127.0615
|1196.456-1216.338
|1164.087
|1223.502-1243.384
|1171.2785
|1243.692-1263.575
|1188.982
|1257.607-1277.4895
|1201.216
|1206.397
|1233.443
|1253.6335
|1267.548
|-
|-
|14
|14
Line 553: Line 639:
|C#
|C#
|''D#''
|''D#''
|1202.23
|1288.234-1309.676
|1213.759
|1288.491-1309.903
|1253.633
|1317.618-1339.026
|1261.377
|1339.361-1360.773
|1280.443
|1354.346-1375.758
|1293.617
|1299.197
|1328.3235
|1350.067
|13565.052
|-
|-
|15
|15
Line 568: Line 649:
|D
|D
|''S''
|''S''
|1288.104
|1380.283-1403.224
|1300.456
|1380.526-1403.467
|1343.178
|1411.733-1434.674
|1351.475
|1435.03-1457.97
|1371.903
|1451.085-1474.026
|1386.018
|1391.997
|1423.204
|1446.5
|1462.556
|-
|-
|16
|16
| colspan="2" |Ep
| colspan="2" |Ep
| colspan="2" |E
| colspan="2" |E
|1373.977
|1472.3015-1496.772
|1387.153
|1472.561-1497.032
|1432.723
|1505.849-1530.319
|1441.5735
|1530.698-1555.168
|1463.363
|1547.824-1572.295
|1478.419
|1454.796
|1518.083
|1542.934
|1560.0595
|-
|-
|17
|17
| colspan="2" |F
| colspan="4" |F
| colspan="2" |F
|1557.82-1583.82
|1459.851
|1564.596-1590.596
|1473.85
|1599.964-1625.964
|1522.268
|1626.366-1652.366
|1531.672
|1644.563-1670.563
|1554.823
|1570.82
|1577.596
|1612.964
|1639.367
|1657.563
|}
|}
== See also ==
* [[17ed5/2]] - equal division of the classic major tenth
* [[17ed7/3]] - equal division of the septimal minor tenth
Retrieved from "https://en.xen.wiki/w/User:Moremajorthanmajor/17edX"